Determine the convergence of an alternating series involving a sine function divided by n squared.

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Convergence of an Alternating Series with Sine

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Determine whether \( \sum_{n=1}^{\infty} (-1)^{n+1} \frac{\sin (\pi/n)}{n^2} \) converges.

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Tests the ability to apply the concept of absolute convergence and the Direct Comparison Test to bound trigonometric terms.

This is a standard problem in a Calculus II course covering infinite series and convergence tests.